Thorstein Veblen’s Theories Applied to a General Equilibrium
Framework
Sophie Wiedijk
Date: 7 July 2016
Student number: 10656502 Thesis supervisor: Andro Rilović Faculty of Economics and Business BSc Economics and Business Specialisation: Economics
Statement of Originality:
This document is written by Sophie Wiedijk, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents
Introduction
4
Chapter 1. Literature review
7
Overview 7
1. Thorstein Veblen’s theories 7
Consumption: The Theory of the Leisure Class . . . 7
Production: The Theory of Business Enterprise and Absentee Ownership and Business Enterprise in Recent Times . . . 10
2. New institutional economics 11 3. Previous research 13 O’Hara (1993): Veblen’s analysis of business, industry, and the limits of capital . . . 13
Bagwell & Bernheim (1996): Veblen effects in a theory of conspicuous consumption . . . 14
Eaton & Eswaran (2009): Well-being and affluence in the presence of a Veblen good . . . 15
Hopkins & Kornienko (2004): Running to keep in the same place: consumer choice as a game of status 17 Cooper, García-Peñalosa, & Funk (2001): Status Effects and Negative Utility Growth . . . 18
4. Implications and conclusion 20
Chapter 2. The Model
21
1. Cooper’s model with one type of labour 21 Consumption . . . 21Production . . . 22
Research and Development . . . 22
Demand functions . . . 23
Monopoly profits . . . 24
Utility growth . . . 27
2. The extended model 29 Consumption . . . 30
Production . . . 31
Research and Development . . . 31
Demand functions . . . 32
Monopoly profits . . . 34
Research intensities . . . 36
Utility growth . . . 38
3. Concluding remarks 40
Chapter 3. Discussion and conclusion
42
1. Summary of results 42 2. Limitations and suggestions 44 3. Conclusion 45 Appendix 49 A.1 Deriving the reaction function for consumer i in peer group k: . . . 49A.2 Demand for normal goods and individual labour supply if xk t = 0: . . . 49
A.3 Aggregate demand for any market state: . . . 50
A.4 Rewriting πs t: . . . 50
A.5 Aggregate profits: . . . 51
A.6 Deriving the wage rate: . . . 51
A.7 The present value of patent-holder profits: . . . 52
A.8 Solving for normal-good sector research employment: . . . 53
A.9 Aggregate demand for any market state: . . . 54
A.10 Aggregate research employment: . . . 55
A.11 Research employment allocated to status-good improvement: . . . 55
Introduction
In 1930, John Maynard Keynes wrote an essay named ’Possibilities for our grandchildren’, in which he de-scribed the state of the economy as he predicted it would be a century later. He proposed that in 2030, standards of living would be eight times higher than at the time of writing. He further assumed that the workweek would be reduced to fifteen hours, which would cause individuals to be worried about a lack of purpose in their lives due to excessive amounts of free time (Keynes, 1930, p.360). With regard to the first prediction, US per capita income was 5.6 times higher in 2010 than when Keynes wrote his essay. Given average annual per-capita growth, in 20 years Keynes’ supposition is likely to materialise. However, although per-capita income has significantly increased, his second prediction does not resemble current labour conditions. Even though there has been a large amount of economic growth in the past decades, people have not increased the amount of time spent on leisure (Akerlof and Schiller, 2015, pp.19-20).
The increase in income does not, on average, seem to have lead to higher levels of well-being either; between 1973 and 2004, average happiness in the the US, as measured by General Social Survey, has largely remained constant even though real GDP per capita has almost increased twofold (Clark, Frijters, & Schields, 2008, p.3). Similar results were obtained through surveys in Japan and parts of Europe (Clark, Frijters, & Schields, 2008, p.4). This increase in income without a corresponding increase in average happiness has been labelled the Easterlin paradox, after the author who first researched this trend in 1974.
The lack of an increase in happiness does not appear to be caused by a lack of consumption; even in times of economic crisis, such as the recession that commenced in 2007-2008, individuals have continued to purchase luxury items such as designer handbags, even when their income would not allow them to in the long run (Nunes, Drèze, & Han, 2001, pp.202-204).
In mainstream economic models, it is generally assumed that increases in income lead to increases in con-sumption, and thus to greater utility. Assuming that utility and happiness have a strong correlation, these models do not seem able to explain the trends described above. The lack of resemblance of these economic theories to actual processes in the economy may be caused by the lack of realism in the assumptions they are based on. Con-sumer preferences are regarded as exogenous and static, such that no explanation for these seemingly irrational decisions and unexpected trends can be inferred from them. In addition to assumptions regarding the proposed rationality of individuals, mainstream models predict efficient economic outcomes, but these predictions do not seem to correspond to the dynamics actually observed.
Therefore, there is a need for an economic theory that can explain these events. Because these occurrences seem to stem from the decisions of individuals, this theory should be able to describe which factors drive con-sumers to make these choices. It may then be possible to explain why, although incomes have increased, hap-piness or free time have not followed suit. In this paper, it is argued that such a theory already exists, and has been proposed in the beginning of the twentieth century by Thorstein Veblen.
Veblen is able to explain why individuals engage in levels of consumption expenditure that do not increase their happiness through his notion of conspicuous consumption. Conspicuous consumption is defined as the consumption of (often expensive) goods that do not provide the consumer with physical satisfaction, but instead
function as evidence of the possession of material wealth. Consumers purchase luxury goods in order to obtain status, based on an interpersonal comparison with others. Concerning production, Veblen explains the recurrence of crises through the dichotomy between ’industry’ and ’business’. Both of these concepts will be discussed in detail later.
Often regarded as the founder of institutional economics, Thorstein Veblen argues that these tendencies or in-stincts that influence the economic behaviour of individuals and firms are institutionally determined. Institutions are thought to constrain behaviour, such that economic outcomes may not necessarily be efficient.
Although Veblen’s theories appear to be useful to elucidate those aspects of economic behaviour that cannot be explained by mainstream economic theories, his work does no longer receive much attention. Currently, the focus of economic theorising is on the design of mathematical models. The interaction of consumer and producer decisions in more than one market is conventionally modelled using general equilibrium models. However, as has been discussed, basic general equilibrium models may lack in their degree of resemblance to empirical events.
Thus, an extension of the general equilibrium framework that includes the institutional constraints proposed by Veblen would be appropriate. In this way, Veblen’s insights can be revived in a framework that is in accord-ance with the methodology that is currently dominant in economic theorising.
In recent years, there has been an increase in research on the relationship between economics and happiness in the field of economics, as well as in psychology, sociology and political science (Clark, Frijters, & Schields, 2008, p.56). However, this research has only sparsely been applied to a general equilibrium framework, which makes a comparison with mainstream economic models difficult. In a small number of studies, Veblen’s concept of conspicuous consumption has been applied to a general equilibrium model. Most of these models regard income as exogenous and do not include Veblen’s insights regarding the production side of the economy. The models that have been developed so far need to be improved. This improvement could possibly be made by including more aspects of Veblen’s theories.
Therefore, this paper investigates whether mainstream general equilibrium models can be improved by in-cluding the insights that Veblen provided a century ago. It may then be possible to assess whether a general equi-librium model can be designed that resembles the economic behaviour that is actually observed more closely. Thus, the question that this research attempts to answer is the following:
How can Thorstein Veblen’s assumptions on the nature of producer and consumer behaviour be applied to a general equilibrium model, and which implications regarding the dynamics of the economy can be inferred from such a model?
This paper adds to existing research in multiple ways. First, it attempts to improve the classical general equilibrium framework by including more realistic assumptions regarding economic behaviour. Second, it ex-tends existing research on conspicuous consumption by including the implications of wasteful spending on the labour supply. It also investigates the effects of the ownership of profit shares and other non-labour income on conspicuous consumption. Additionally, Veblen’s theories on production are included in the general equilibrium model. Finally, the broader aim of this research is to show that mathematical modelling and theoretical insights based on real-life observation, instead of being mutually exclusive, can reinforce one another.
To answer the research question, a literature review will be combined with the extension of an existing model. The first chapter contains the literature review, which consists of four sections. The first section gives an overview of Veblen’s theories regarding production and consumption. In the next section, this research is
placed in a theoretical framework by discussing the core assumptions and research methods proposed by new institutionalism. In the third section, an assessment is made of the extent to which previous research has thus far succeeded in including Veblen’s assumptions into economic models and in which areas improvements can be made. The fourth section concludes with a discussion of how the findings obtained in this chapter will be used to answer the research question.
The second chapter commences by explaining the dynamics of an existing model, in which a number of Veblen’s insights are included. The second section then extends this model by including assumptions on income and expenditure. The final section concludes.
The final chapter will provide the conclusion, as well as a discussion of the findings obtained through the model and its limitations, and provides recommendations for further research.
Chapter 1. Literature review
Overview
This chapter consists of four sections. The first section discusses Thorstein Veblen’s insights on consumption, as explained in The Theory of the Leisure Class (Veblen, 1899), and production, as discussed in The Theory of
Business Enterprise (Veblen, 1904) and Absentee Ownership and Business Enterprise in Recent Times (Veblen,
1923). The contents of these books are reviewed, after which a summary of the relevant assumptions and insights obtained is listed.
The second section provides a discussion of the manner in which this research fits into the theoretical frame-work provided by new institutional economics.
The third section reviews previous research in which an attempt is made to include some of Veblen’s assump-tions regarding consumption and production into an economic model to assess if and how this can be improved. The fourth and final section of this chapter concludes and discusses the implications of the findings in the previous sections for the manner in which the research question will be answered.
1. Thorstein Veblen’s theories
Veblen argues that economic behaviour has social foundations, as determined by human instincts. These in-stincts are partially institutionally determined (Veblen, 1899). On the one hand, individuals possess inin-stincts that further the collective welfare of society. The instinct of workmanship is mechanical in character and fo-cuses on technological innovation and productive efficiency (Veblen, 1899, p. 15). It is complemented by the parental bent, which relates to the tendency to care for other individuals (Veblen, 1914, p. 26) and the instinct of idle curiosity, which is the urge to find the answers to questions that do not directly further the self-interest (Veblen, 1914, p. 85). These instincts conflict with ceremonial instincts, that negate the collective welfare to further individual gain. These are the instinct of predation, which refers to the tendency toward aggression and plunder (Veblen, 1899, p. 225), the instinct of emulation, which is the tendency for status-based comparison (Veblen, 1899, p. 236), and the pecuniary instinct, which causes individuals to make judgements based on mon-etary standards (Veblen, 1899, pp. 237-238). Veblen uses these conflicting instincts to explain the economic behaviour of both consumers and producers, as will be discussed below.
Consumption: The Theory of the Leisure Class
In The Theory of the Leisure Class (1899), Thorstein Veblen analyses the economic behaviour of consumers. He commences his disquisition with a discussion on the manner in which industrious and ceremonial instincts have developed over the advancement of human kind. He then turns to an analysis of what these instincts
imply with regard to the economic behaviour of consumers. Here, those insights that are relevant to the model developed in this research are discussed.
Cultural development
Veblen argues that according to neoclassical economic theory, acquisition happens for economically legitimate reasons. It is assumed that “the end of acquisition and accumulation is conventionally held to be the consumption of the goods accumulated” (Veblen, 1904, p. 13). However, Veblen claims that this was only true in the early, inefficient stages of industry.
In modern industry, he argues, the core motivation for ownership is emulation. Wealth, originally seen as evidence of the instinct of workmanship, becomes valuable in itself and is established as the conventional basis for esteem. It is no longer enough to possess wealth or power. Rather, this possession must be put in evidence. Members of the higher classes abstain from industrious labour, such that leisure becomes “the conventional mark of superior pecuniary achievement and the conventional index of reputability” (Veblen, 1904, p. 19). Therefore, a leisure class emerges, which consists of those individuals who possess the highest levels of wealth and who do not engage in industrious labour (Veblen, 1904, p.12).
Conspicuous leisure and conspicuous consumption
As the number of individuals in society increases, an industrial community develops, with the rules and customs governing ownership increasing both in scope and in consistency (Veblen, 1904, p. 21). Wealth is accumulated and the leisure class develops further, such that a differentiation arises within the class, creating a system of ranks and grades. This differentiation is made stronger by the inheritance of wealth. Those in the middle classes affiliate themselves by emulating the consumption of those who rank above them in terms of reputability (Veblen, 1904, p. 37).
Veblen continues his explanation by arguing that “the leisure class stands at the head of the social structure in point of reputability; and its manner of life and its standards of worth therefore afford the norm of reputability for the community (...). The observance of those standards becomes incumbent upon all classes lower in the scale” (Veblen, 1904, p. 40).
As society develops further and property becomes held by a relatively smaller share of the total population, the conventional standard of wealth of the upper class rises (Veblen, 1904, p. 27). A new comparison is made, based on higher levels of wealth, such that the former standard for sufficiency ceases to please. Thus, most members of society will be chronically dissatisfied. Veblen explains this in the following manner: “If (...) the incentive to accumulation were the want of subsistence or of physical comfort, the aggregate economic wants of a community might conceivably be satisfied at some point in the advance of industrial efficiency” (Veblen, 1904, p. 16). However, as some wants are based on reputation, determined by interpersonal comparison, this does not happen.
Thus, because as industry becomes more efficient, more is produced than is necessary for subsistence, all but those who belong to the poorest classes accumulate goods as evidence of the possession of wealth (Veblen, 1904, p. 14).
The pecuniary standard of living
Conspicuous consumption also undergoes a specialisation in the quality of the goods consumed, such that failure to consume the socially appropriate quantity and quality of goods becomes a sign of inferiority (Veblen, 1904, p. 36). Goods are regarded to be desirable roughly in proportion to how wasteful impractical they are (Veblen, 1904, p. 59). Society’s discrimination of what is legitimately tasteful is thus guided by the expensiveness of a product, or equivalently, the amount of wasteful labour-efforts required to produce it (Veblen, 1904, p. 60).
It must be noted that ‘wasteful expenditure’ is labeled as such by Veblen because it does not serve the aggregate welfare of society. It is thus not wasteful from the point of view of the individual consumer that chooses it (Veblen, 1904, p. 46). Wasteful expenditure is flexible upward as wealth levels increase, but once an individual gets used to a certain level of conspicuous consumption, this consumer will be reluctant to reduce expenditures, even if this is necessary (Veblen, 1904, pp. 48-50).
One of the main points Veblen makes is that an increase in productive efficiency will lead to more conspicu-ous consumption, but not necessarily to an easier life for the working classes: “As increased industrial efficiency makes it possible to procure the means of livelihood with less labour, the energies of the industrious members of the community are bent to the compassing of a higher result in conspicuous expenditure, rather than slackened to a more comfortable pace” (Veblen, 1904, p. 51). Veblen goes on to predict that the share of wealth individuals within a class will spend on conspicuous waste is as high as their earning capacity will permit, with a constant tendency to go higher. The activities of individuals will then be directed towards the largest possible acquisition of wealth (Veblen, 1904, p. 52).
Increased mobility and communication have added to the ease with which social comparisons can be made, such that social emulation can be expected to expand (Veblen, 1904, p. 63).
Veblen’s insights regarding consumption
In summary, as productive industry has become more efficient, most members of society have become able to consume more than they need for subsistence.
The character of wealth has thus changed from being the evidence of productive efficiency to being a good to be attained in itself. Individuals aim to signal the level of their accumulated wealth to others by engaging in conspicuous leisure. Namely, only those individuals that are relatively affluent can afford to refrain from engaging in productive labour.
As the time spent on conspicuous leisure may be difficult to convey to others , conspicuous consumption, defined as expenditure on goods that do not increase the individual’s physical well-being, has become the most effective proof of pecuniary ability.
The highest class in society, the leisure class, consumes the largest share of those goods that provide the highest reputability. All lower classes emulate the consumption behaviour of those classes above them.
Production: The Theory of Business Enterprise and Absentee Ownership and Business
Enterprise in Recent Times
The distinction between industry and business
Veblen argues that the characteristic features of the modern industrial system are the machine process on the one hand and investments for profit on the other. The scope of industry is given by the machine, which sets the pace for the rest of the industrial system. Production is organised by the business enterprise. Business forces have thus become a controlling factor in industry, because through the mechanism of investments and markets, these forces “control the plants and processes, and set the pace and determine the direction of movement for the rest” (Veblen, 1904, pp. 1-2).
Thus, Veblen makes a distinction between industry and business in the industrial system. Industry is driven by the instinct of workmanship and oriented to the expansion and efficiency of mechanical production. Business, on the other hand, is executed by those who own the wealth that has been invested in corporations. Business is driven by the accumulation of profits, defined as “the capitalised value of (...) presumptive earnings” (Veblen, 1923, p. 219). The activities of business are unproductive of output and include finance, banking, accounting, sales, marketing, and pricing (Veblen, 1904, p. 106).
The tendencies of capitalism
Veblen uses his distinction between the interests of business and industry to develop a business-cycle theory, in which he analyses the tendencies of capitalism in the long run.
Overproduction and depression
Capital has a tendency for ‘large-scale enterprise’, which, if market conditions are fairly competitive, implies that firm profits decrease over the long run, which leads to low investment, instability, and business recession. As posed by Veblen, “(...) depression is normal to the industrial situation under the consummate regime of the machine, so long as competition is unchecked” (Veblen, 1904, p. 255).
Depression is caused by two processes. The first is an increasing efficiency in industry, which causes over-production as the extension of the technology throughout industry results in a greater supply of goods under conditions of free competition (Veblen, 1904, p. 264). Low prices then reduce business profits. The second process that leads to depression is “the interdependence of the several lines of industrial activity”, which implies that crises spread throughout the system quickly (Veblen, 1904, p. 264). Thus, in a system where “workmen do not and cannot own or direct the the industrial equipment and processes, so long as ownership prevails and industry is to be managed on business principles” (Veblen, 1904, p. 265), there will be a tendency for depression.
Collusion and the promotion of wasteful expenditure
Veblen continues his disquisition by arguing that business interests will attempt to resolve this tendency for low profits and depression in either of two ways. The first way is through the promotion of the unproductive consumption of goods, or conspicuous consumption. The second manner in which business interests can aim to increase profits is through “an elimination of that ‘cutthroat’ competition that keeps profits below the ‘reas-onable’ level” (Veblen, 1904, p. 255). Veblen observed the implementation of these ‘solutions’ in the early mid-twentieth century. The problems of overproduction were, to some extent, overcome by collusion that led to a more concentrated market. Banks, credit institutions, and investment banks reinforced business interests. With a decrease in competition, it became possible to limit output, such that prices and profits could remain high. Complemented by marketing efforts and financial institutions, overproduction could be moderated. Absentee ownership, which is the ownership of firms by agents who do not engage in the production carried out by those firms, was transferred from affluent individuals to banks, investment houses, and insurance companies (Veblen, 1923, pp. 211-213). This implies that business interests became more concentrated and better organised.
Excessive waste and instability
However, this response to overproduction by business interests could lead to an increase in unproductive activities large enough to introduce uncertainty into the system. Veblen stated that a “persistent excess of parasitic and wasteful efforts over productive industry must bring on a decline” (Veblen, 1904, pp. 64-65). Collusion and conspicuous consumption could lead to excessive waste, which promotes instability, uncertainty, and the risk of a major crash. As long as conspicuous consumption and collusion successfully work together, there is an expansion of credit, and higher values are placed on firms’ shares. The increased value of capital can then serve as collateral, such that credit expands further. At some point, however, fears will arise that the prices of immaterial capital goods and their actual earning capacity don’t correspond with each other. This would then lead to a crash.
Veblen’s insights regarding production
In summary, Thorstein Veblen makes a distinction between industry, which is productive and aims for mechanical efficiency, and business, which is unproductive of output and aims for pecuniary gain. These contradictory interests will lead to recurring crises. Capital has a tendency for the accumulation of profits, as well as for the expansion of unproductive activities and business practices.
The tendency for profit accumulation leads to crises in the following way. The mechanical process of pro-duction is essential to capital, but it leads to limits when propro-duction, through innovation, expands too rapidly relative to the depth of the market. This will then lead to overproduction and depression.
The tendency for the expansion of business activities can lead to crises since it has the tendency to be so wasteful as to over-exploit industry, which promotes uncertainty and instability.
2. New institutional economics
In this section, the thesis will be placed in a theoretical framework. The works of North (1986) and Brinton and Nee (1998) will be discussed to argue why and to which extent the theoretical fundamentals of new institutional economics are in line with the aim and method of this research.
Thorstein Veblen’s theories are part of the school of thought called institutional economics. This theoretical perspective focuses on understanding how institutions and evolutionary processes shape economic behaviour (Stilwell, 2012, pp.212-213). This can be exemplified by Veblen’s dichotomy of ceremonial and industrious or technological instincts referred to in the first section, which are assumed to be partially shaped by institutions and which at the same time shape the evolutionary processes that determine the economic behaviour of individuals. Thus, a model that includes Veblen’s insights can be expected to be in line with the theoretical fundamentals of institutional economics. However, as this research intends to apply Veblen’s theories to a neoclassical general equilibrium framework, its successor, new institutional economics, is thought to be more useful in providing the theoretical fundamentals underlying the model.
In The New Institutional Economics (1986), Douglass C. North provides an overview of the content and methods of new institutional economics.
North defines institutions as “regularities in repetitive interactions among individuals which limit the range of choice in individual interaction” (North, 1986, p. 231). He states that the theoretical framework of new insti-tutional economics should be capable of integrating neoclassical theory in an analysis of how institutions affect the choices available to individuals. By doing this, the choices actually available to agents can be determined and the manner in which institutions change over time can be analysed (North, 1986, p. 230).
With regard to this research, these premises will be adhered to. From neoclassical theory, the objective functions, optimisation methods and the basic structure of general equilibrium models are utilised. These are then used to analyse how the ceremonial and industrious instincts of individuals affect and constrain their behaviour. North argues that, in order to make normative statements on public policy, these statements must be based on positive theory (North, 1986, p. 235). North (1986) does not indicate which criteria would be useful to assess policy options. In this respect, the usefulness of this paper is limited. However, if this research is able to explain the way in which the dichotomy of instincts as proposed by Veblen shapes economic behaviour, then this could be a step towards the positive theory to base normative statements on. In other words, it could aid in predicting the outcome of actions within this institutional framework, which is a first step towards deciding which of these outcomes is most desirable.
In addition to the overview provided by North (1986), Brinton and Nee (1998) argue that the core concept in new institutionalism is choice under constraints (Brinton & Nee, 1998, p. 8). Thus, individual choice can still be used as the driver of economic outcomes, which implies that the methods of neoclassical economics remain useful. Their indication that institutions constrain the choices of actors then implies that the assumptions made by Veblen can be introduced to a general equilibrium model as constraints in consumers’ and firms’ decision-making process.
Additionally, Brinton and Nee note the usefulness of game theory in explaining the dynamics of choice with constraints. However, game theory does not explain how these constraints come about (Brinton & Nee, 1998, p. 5). Game theory is mainly useful with regard to modelling conspicuous consumption. When Veblen argues that conspicuous consumption occurs due to interpersonal comparisons based on pecuniary status, this implies the presence of strategic interaction, as the outcome of one individual’s choices depend on the consumption decisions made by others. Veblen’s theories then complement game theory by providing an explanation of how the negative externality consumers impose on one another arises.
Brinton and Nee further argue that the field of economics can be improved through new institutionalism by obtaining the “theoretical and empirical findings specifying causal mechanisms at the organisational and
environmental levels” (Brinton & Nee, 1998, p. 11). Thus, by adhering to this theoretical perspective, neoclas-sical models can be made more realistic without having to lose their practical usefulness in modelling economic processes.
Taking Veblen’s institutional economics and incorporating it in a general equilibrium framework can, as a method of analysis, thus be said to be in line with new institutional economics.
3. Previous research
In this section, previous research on economic behaviour that utilises Veblen’s insights is discussed. O’Hara (1993) has developed a model which illustrates the dynamics described in Veblen’s Theory of Business Enterprise and Absentee Ownership and Business Enterprise in Recent Times. Additionally, a number of models has been developed that incorporate the concept of conspicuous consumption. These models have been designed by Bagwell and Bernheim (1996), Eaton and Eswaran (2009), Hopkins and Kornienko (2004), and Cooper, García-Peñalosa and Funk (2005). Each of these models will briefly be discussed. An assessment will be made of the contributions provided by each source to understanding economic processes through Veblen’s theories, as well as their limitations or shortcomings.
O’Hara (1993): Veblen’s analysis of business, industry, and the limits of capital
O’Hara (1993) studies Veblen’s insights regarding production by developing a simple model. He then uses this model to explain the manner in which the limits to capital have developed over time. Finally, he develops a criticism of Veblen’s theory on the dichotomy between industry and business.
O’Hara bases his model on the assumption that corn is the basic commodity, which functions as both an input as an output of production. Corn also functions as the unit of exchange in the economy (O’Hara, 1993, p.96). As in The Theory of Business Enterprise, the two main activities in production are business, which is unproductive of corn and instead concerns itself with occupations such as marketing and finance, and industry, which is productive of corn and corn-using manufactures (O’Hara, 1993, p.96).
O’Hara develops a model to show that there are three dimensions to the limits to capitalist production. These are the actual degree of workmanship, the possibility of overproduction, and the ratio of productive to unproductive activities (O’Hara, 1993, p.96).
This model shows that production is limited by industry. Furthermore, he shows that when business under-exploits industry, such that output grows faster than demand, a depression results. On the other hand, overex-ploitation of industry by business, where conspicuous waste is excessively promoted and unproductive activities take primacy over productive ones, results in instability and crises (O’Hara, 1993, p.105). These limits are vari-able over time and qualitative in nature, such that they are represented by bars or areas, rather than by a set of points in a line (O’Hara, 1993, pp.105-106).
The model provided by O’Hara is useful in illustrating Veblen’s insights regarding production schematically. However, the limits or bars he describes are, as he indicates, qualitative rather than quantitative in nature. This means that O’Hara’s model, however useful in illustrating the process of capitalist production and its tendencies, does not have anything to say about the amount of overproduction or waste that has to be present to reach either limit.
The formulas in his model are designed such that they indicate how the surplus from production is distributed between industry and business, and thus to show the level of exploitation. This is useful for the explanation of the tendencies and limits of capital, but make it rather difficult to incorporate the way in which consumer decisions affect this process. Higher levels of wasteful expenditure are assumed to eventually lead to the overexploitation of industry by business, but because consumption is not explicitly included in this model, the dynamics of this process cannot be determined from it. In order to design a model that includes Veblen’s theories on production as well as consumption, this model is thus not appropriate.
Additionally, in order to compare the implications of neoclassical economics with the implications provided by Veblen’s theories, developing a model within the framework of a general equilibrium model makes it possible to determine explicitly if and at which points the two interpretations of economic behaviour differ. Because this model does not use a general equilibrium framework, making a direct comparison is difficult.
Thus, O’Hara (1993) provides useful insights into Veblen’s views regarding production. The model is, however, limited with regard to this research, as it does not incorporate consumer decisions. A model of Veblen’s theories would thus have to yield results that are in line with this paper, but also include how consumer behaviour is affected by the instincts Veblen describes.
Bagwell & Bernheim (1996): Veblen effects in a theory of conspicuous consumption
Bagwell and Bernheim (1996) argue that because, according to Veblen, individuals enhance their status through material displays of wealth, utility should be defined over consumption and status. Because conspicuous con-sumption is intended to provide evidence of pecuniary wealth, the relation between price and status should result from signalling (Bagwell & Bernheim, 1996, p.350). This paper then investigates under which conditions Veblen effects, defined as the willingness to pay higher prices for functionally equivalent goods (Bagwell & Bernheim, 1996, p.349) arise from the desire to signal wealth.The authors assume that there are two types of households, (H and L) that differ in their wealth levels (R), such that RL < RH. Households only know their own wealth level, which they signal to others by
consump-tion of a conspicuous good. The conspicuous good is denoted x, and has quality q ∈ [q,q]. The inconspicuous good z is of fixed quality and is consumed privately, such that it can not serve as a signal of wealth (Bagwell & Bernheim, 1996, p.352). Each household has preferences over its total quality-weighted conspicuous con-sumption x (Bagwell & Bernheim, 1996, p.353). Consumers also obtain utility from concon-sumption of z and an action ρ, taken by the representative social contact. Thus, total utility of type i is given by Ui(x, z, ρ) (Bagwell
& Bernheim, 1996, p.353).
Conspicuous consumption is observed by a social contact, who obtains payoff φ(R, ρ), where R is the wealth of the household with which it interacts (Bagwell & Bernheim, 1996, p.353). Social contacts choose the value of ρ that maximises expected payoffs given R and their assessment of the probability that the household is of type H (Bagwell & Bernheim, 1996, p.353).
The conspicuous good can be provided by a large number of firms. All firms can produce the same range of qualities. Each firm produces a single product, which is branded so that social contacts can identify the manufacturer (Bagwell & Bernheim, 1996, pp.353-354).
Bagwell and Bernheim show that if the single-crossing property holds, which means that the indifference curves of both types of households cross only once (Bagwell & Bernheim, 1996, p.357), Veblen effects do not arise. Namely, all households buy the conspicuous good at quality-weighted price p. This happens because
type-L households choose this price in any equilibrium (Bagwell & Bernheim, 1996, p.356). Then, type-H households can purchase goods with a higher price, or a larger amount of goods at the same price. Both options signal to the social planners that they have a higher R, but the latter option makes them better off (Bagwell & Bernheim, 1996, p.358). Thus, there are no Veblen effects, due to the fact that households signal their wealth through quantity, not by paying a higher price for the same goods.
However, if the indifference curves of both types of households are tangential to each other, the authors find that type-H households will pay a higher price for the conspicuous good than type-L households (Bagwell & Bernheim, 1996, pp.361-362). This also implies that some firms are able to charge a price above marginal cost. According to Bagwell and Bernheim, this tangency property can arise in three possible scenarios. The first scenario arises when consumers borrow to finance expenditure, such that there are bankruptcy constraints (Bagwell & Bernheim, 1996, p.364) . The second scenario arises when conspicuous expenditure is deductible for the purpose of computing personal income taxes (Bagwell & Bernheim, 1996, p.366). The last possibility is the case in which type-L households receive greater utility from conspicuous consumption than type-H households, for instance because of satisfaction derived from ’acting rich’ (Bagwell & Bernheim, 1996, p.366).
This paper provides insights about conspicuous consumption as a signalling tool. It allows for a distinction between classes with different incomes with regard to their conspicuous consumption. It shows that conspicuous consumption can allow firms to charge prices above marginal cost, which corresponds to the insights in The
Theory of Business Enterprise. The result that the presence of Veblen effects is more plausible when consumers
are allowed to borrow, deduct conspicuous consumption from taxable income, or when less affluent classes gain additional utility from acting rich are in line with Veblen’s theories and make this research relevant to real-life processes.
However, the analysis carried out in this paper relies on the assumption that consumers signal their wealth because there is imperfect information. According to Veblen, signalling wealth levels is only one of the reas-ons to engage in creas-onspicuous creas-onsumption. Additionally, individuals may aspire for status as an end in itself (Veblen, 1899). Consumers get satisfaction from engaging in more conspicuous waste than others, even when they know those others have higher wealth levels, because the perceived need for conspicuous waste has become internalised in individuals’ instincts (Veblen, 1914, pp.235-238). Thus, a stronger result would be obtained by a model that shows the presence of social emulation without requiring the presence of incomplete information. Furthermore, this model does not provide any information on the manner in which households obtain their wealth or on how they decide on the amount of labour they provide. This also means that, apart from the insight that some firms make positive profits, the production side of the economy does not correspond to Veblen’s theories in this model.
Eaton & Eswaran (2009): Well-being and affluence in the presence of a Veblen good
Eaton and Eswaran (2009) use Veblen’s notion of conspicuous consumption to explain why increases in per capita income have not led to corresponding increases in average well-being by developing a series of general equilibrium models (Eaton & Eswaran, 2009, p. 1088).First, the authors consider a ’standard model’, in which consumer preferences are defined over leisure (xi),
a Veblen good, which is only valued in terms of relative consumption (vi), and a normal good (yi) ((Eaton &
They assume there is a continuum of identical consumers. The representative individual’s utility function is Ui(xi, vi, yi) = F (xi) + G(yi) + D(vi− v) + R(vi/v),
where v is average consumption of the Veblen good (Eaton & Eswaran, 2009, p. 1090). Each individual is endowed with one unit of time (Eaton & Eswaran, 2009, p. 1090).
The authors further assume that consumption goods are produced using only labour under constant returns. One unit of labour is assumed to produce one unit of either good. Because the competitive equilibrium price of labour is defined as w, the competitive equilibrium price of both goods and the wage rate must equal 1 (Eaton & Eswaran, 2009, p. 1090).
Because Ui is decreasing in v, consumers impose a negative consumption externality on each other. A
social planner would recognise that as consumers are identical, in equilibrium v = vi; the Veblen good does not
contribute anything to Ui. The optimal consumption of this good would thus be vi = v = 0. However, to any
individual consumer, this is not a Nash equilibrium.
The authors find that “as productivity increases without bound, the equilibrium consumption of leisure ap-proaches zero, that of the standard good apap-proaches a finite upper bound, and that of the Veblen good is unboun-ded” (Eaton & Eswaran, 2009, p. 1092).
The analysis is continued by introducing the provision of a public good. In a similar manner as in the standard model, they find that as productivity increases, spending on both the public good and the standard good approaches a finite upper bound, whereas time allocated to leisure approaches zero and consumption of the Veblen good increases without bound (Eaton & Eswaran, 2009, pp.1096-1097).
Next, the authors assume that there are two types of leisure, namely private and social leisure. They propose to include a good called community, which is produced by individuals’ voluntary choices of social leisure, and the provision of which imposes a positive externality on all individuals (Eaton & Eswaran, 2009, p. 1098). It is then found that as productivity increases without bound, both types of leisure approach zero, consumption of the standard good approaches its finite upper bound, and spending on the Veblen good increases without bound (Eaton & Eswaran, 2009, p. 1100).
Thus, in each of the models, increasing productivity has the consequence of the Veblen good crowding out all utility-increasing goods and activities (Eaton & Eswaran, 2009, p. 1101).
In this model, as individuals become more affluent, at some point they will no longer increase their spending on normal goods. Once sufficient amounts of normal goods are consumed for subsistence, consumers will use the remainder of their income on conspicuous consumption. This result, as well as the proposition that leisure approaches zero follows Veblen’s theories, as discussed in section 1.
This model provides insights into the dynamics of consumer behaviour as productivity increases and its implications are in line with the predictions made by Veblen. However, it does not consider the dichotomy between business and industry. It neither provides an indication of the factors that would cause productivity to increase.
Hopkins & Kornienko (2004): Running to keep in the same place: consumer choice as
a game of status
Hopkins and Kornienko (2004) develop a model in which individuals’ concern for status takes the form of a simultaneous-move game.
They assume the presence of a continuum of agents, who are identical except in terms of income. Each agent is endowed with income z, which is an independent draw from income distribution G(z) (Hopkins & Kornienko, 2004, p.1088). Agents decide how to allocate income between a status good (x) and a normal good (y). Choices of x are aggregated over agents in distribution F (·), where F (x) represents the mass of individuals for which consumption of the status good is at most x. Thus, for an individual that consumes x, F (x) gives the expected frequency with which she can make favourable interpersonal comparisons (Hopkins & Kornienko, 2004, p.1088).
Status is defined as
S(x, F (·)) = γF (x) + (1 − γ)F−(x) + α,
where γ ∈ [0, 1] is a constant that represents a decrease in status resulting from ’ties’ andF−(x) is the mass of
individuals with consumption strictly less than x. α ≥ 0 is a constant that represents a guaranteed minimum level of status (Hopkins & Kornienko, 2004, pp.1088-1089).
Each consumer has a utility function that depends on the level of own consumption and on status: U(x, y, S(x, F (·))) = V (x, y)S(x, F (·)),
where V (x, y) is a conventional utility function that is strictly increasing in the consumption of both goods (Hopkins & Kornienko, 2004, p.1089).
Each consumer faces a budget constraint px + y ≤ z, where p is the price of x and where the price of y is used as the numeraire (Hopkins & Kornienko, 2004, p.1089).
Hopkins and Kornienko find that in the symmetric Nash equilibrium, an individual’s status, given by her position in the consumption distribution, is the same as her position in the income distribution (Hopkins & Kornienko, 2004, p.1091). This implies that spending on x has no impact on status. Indeed, in the cooperative case, in which each consumer disregards status and simply maximises V (x, y), status is also determined by the consumer’s position in the income distribution, but spending on x is lower, which implies that this outcome is Pareto-superior. However, the cooperative case does not constitute a Nash equilibrium, as any individual consumer could increase their status and thus their utility by unilaterally increasing consumption of the status good (Hopkins & Kornienko, 2004, pp.1091-1092).
Hopkins and Kornienko show that an increase in average income may increase conspicuous consumption and could even be consistent with a decrease in social welfare (Hopkins & Kornienko, 2004, p.1095).
The authors further propose that a division of the population of consumers into different classes, or ranges of z, yields the result that an increase in income equality between classes typically implies a greater density of consumers in the middle class. This increases incentives to differentiate oneself. Therefore, those in the middle class increase spending on x (Hopkins & Kornienko, 2004, p.1096).
This paper provides a method for modelling conspicuous consumption that shows how social emulation can be present even under conditions of perfect information. The possibility to analyse the implications of income distribution among classes also shows that, as Veblen predicted, increased income equality and increased average
incomes might have the undesirable effect of increasing conspicuous consumption by facilitating interpersonal comparisons.
However, the assumption that income is exogenous limits the usefulness of this paper. Namely, it makes it impossible to determine the effects of conspicuous consumption on the amount of labour provided by con-sumers. Both the exogeneity of income and the absence of a production sector imply that Veblen’s theorising on production is not analysed by this model.
Cooper, García-Peñalosa, & Funk (2001): Status Effects and Negative Utility Growth
Cooper et al. (2001) provide a dynamic model that includes both conspicuous consumption and the distribution of labour. Labour is allocated between the production of output, technological innovation to improve the quality of normal goods, and ’prestige innovation’ to increase the desirability of status goods. This model will be fully discussed in the next section, as it will be shown that it is suitable as a template model that will be extended to answer the research question. Here, an overview of the assumptions underlying this model and the general results obtained will be discussed.The authors assume that each period, consumers allocate their spending between normal goods (y) and status goods (x). Both goods are produced using unskilled labour (L) as the only input (Cooper et al., 2001, p.647).
The L + H consumers in the economy are arranged into peer groups, where each peer group consists of consumers with identical incomes. Consumers have preferences such that they obtain direct utility from the consumption of y. Utility obtained from the consumption of x depends on the total difference in the consumption of x by others in the individual’s peer group (Cooper et al., 2005, p.646).
The quality of each good can be improved by allocating skilled labour (H) to R&D. In the normal-good sector, innovation implies an improvement in the good’s quality. In the status-good sector, however, innovation leads to a higher prestige level, which implies that R&D efforts in this sector have the characteristics of marketing and advertisement activities that increase the perceived desirability of these goods (Cooper et al., 2001, p.647). The level of R&D employment in a sector determines the probability of innovation occurring in that sector. If an innovation occurs in either sector, the firm that succeeds in innovation obtains a patent. This patent lasts for only one period and, as will be shown in the next section, provides this firm with positive profits. All other firms obtain profits equal to zero (Cooper et al., 2001, pp.647-648).
Each period, consumers save fraction s of their income and spend the remaining fraction on consumption. The only asset in the economy is a claim on future profits, so in equilibrium, savings in period t equal research expenditures in that period (Cooper et al., 2001, pp.645-647).
Cooper et al. show that a higher quality of status goods reduces utility. This is explained by noting that higher prestige innovations make conspicuous consumption more desirable, such that demand for status goods increases. Normal-good consumption is foregone to be able to spend more on status goods, but when all con-sumers increase their status-good expenditure, they do not obtain any additional utility (Cooper et al., 2001, p.653). Additionally, agents with larger peer groups are found to obtain a lower level of utility for a given prestige value (Cooper et al., 2001, p.653).
The authors further show that innovation determines the average rate of growth of the utility function. Changes in prices that occur due to this innovation have a temporary effect on utility, as patents and thus price increases only last for one period (Cooper et al., 2001, p.654). Utility grows when y is improved, but falls when x is improved. Utility growth is shown to be strictly decreasing in the number of researchers employed in the
status good sector. Furthermore, the long-term growth of utility is negative, as the reallocation of researchers to the status-good sector will continue until all researchers are employed in it (Cooper et al., 2001, pp.655-656).
This model uses insights from Veblen’s theories on both consumption and production. With regards to consumption, the strategic behaviour of consumers is modelled such that the dynamics of social emulation can be understood. The division of consumers into peer groups allows for the comparison of consumers in different classes. It also provides implications for the size of consumers’ peer groups, which is in line with Veblen’s theories. With regard to production, the authors explain the difference between normal-good innovation and the innovation of status goods, which closely resembles the distinction between industry and business activities set out in The Theory of Business Enterprise. Including both production and consumption in this way then makes it possible to show how conspicuous consumption furthers business interests and vice versa. Because this is a dynamic model, processes and trends can be analysed, which is appropriate when analysing Veblen’s evolutionary theories. For these reasons, this is the model that will be extended in the next chapter.
However, there are some limitations to this model. It implies that income is exogenously determined, making it impossible to assess the total amount of labour consumers decide to provide in order to engage in normal or conspicuous consumption. Additionally, no implications about the effects of absentee ownership on production can be made, because shares in firms by households are not explicitly defined.
4. Implications and conclusion
By comparing the implications of Veblen’s theories on production and consumption to the results obtained in existing research within the new institutionalist research agenda, it can be assessed which assumptions and methods are useful for the design of a general equilibrium model that incorporates Veblen’s insights.
Several models have successfully incorporated the concept of social emulation by modelling consumer de-cisions as a strategic game. Bagwell and Bernheim (1996) model conspicuous consumption as a tool to signal wealth, but require the presence of imperfect information, which makes the results obtained in their paper lim-ited in those instances when individuals do have information regarding each other’s wealth levels. Eaton and Eswaran (2009) do not require incomplete information and include consumers’ decisions regarding labour and leisure. However, they analyse how increases in productivity affect consumer choices without indicating how these productivity increases come about. Hopkins and Kornienko (2004) define status over a consumption distri-bution to analyse how differences in the income distridistri-bution affect conspicuous consumption and social welfare. However, they assume incomes are drawn from a distribution that is exogenous to the model, so they cannot provide insights on the way in which this income distribution comes about. Cooper et al. (2001) model consump-tion as based on comparisons within an individual’s peer group. This matches Veblen’s insights to the extent that consumers get no additional utility if they engage in the same amount of conspicuous consumption as others in their class, whereas their utility increases if they consume more than others in their class. Namely, as proposed by Veblen, individuals attempt to mimic the consumption of those in the classes above them by consuming more than the members of their own class do. This is the process that Veblen called social emulation. Cooper et al. (2001) also model the division of productive and innovative labour over the production and improvement of normal goods and status goods, which resembles the dichotomy between industry and business. However, they do not model how consumers’ incomes are determined by their provision of labour or their ownership of shares in profits.
Thus, for the model developed in this paper, the model by Cooper et al. (2001) is found to be most useful. The limitations of this model will be attempted to be resolved by assuming there is only one type of labour, supplied by consumers, which will be allocated between production and innovation in a normal-good and a status-good sector. The wages consumers obtain through this provision of labour and their shares in firms’ profits, as well as other non-labour income will then determine the budget consumers have available for consumption expenditure.
Chapter 2. The Model
This chapter consists of three sections. In the first section, the model by Cooper et al. (2001) will be discussed. In the main text of this paper, it is assumed that there are two types of labour, where high-skilled labour can only be used for innovation, whereas low-skilled labour is used in production. Because several assumptions will be added in the extension to this model, the model that is explained here is based on the assumption that there is only one type of labour, which can be employed in both production and innovation. The authors provide this version of the model in the appendix to their paper. After the dynamics of Cooper’s model have been understood, it will be used as the basis for a new model, which is set out in the second section. Several assumptions regarding consumers’ income and expenditure are added. Namely, individuals will be assumed to obtain income through their provision of labour, by means of the ownership of shares in firms’ profits, and from other non-labour sources of income. The final section concludes.
1. Cooper’s model with one type of labour
In this section, the original model as set out by Cooper et al. (2001) will be discussed in order to obtain an understanding of its dynamics. First, the assumptions and functions underlying the model are explained, after which the model is solved. Finally, an indirect utility function is derived in order to assess the evolution of utility over time in the presence of conspicuous consumption and business activities.
There are assumed to be two final-good sectors in the economy: a normal-good sector, denoted y, and a status-good sector , denoted x. The current period is indicated by t. As in Grossman and Helpman (1991), each good can be provided in a countably infinite number of qualities, where quality ν of the normal good equals qv= (γ)ν, with γν >1 . For quality level qvto be attained, the normal good is required to be improved through
the successful use of R&D ν times after t = 0. qtdenotes the quality of the normal good with the highest quality
in period t. Likewise, the status good has prestige value aσ = (γs)σ, attained by successfully improving it σ
times after t = 0. atthen denotes the status good with the highest prestige value at time t (Cooper et al., 2001,
p.645).
Labour (L) can be used for either R&D or production. Demand for labour in the R&D sector, Ht, consists of
labour used for improving normal goods (Hn
t) or for business practices such as marketing and advertisement in
the status-good sector (Hs
t). Labour can also be used in either production sector, where (Dnt) and (Dts) denote
the labour used in the production of normal goods and status goods, respectively (Cooper et al., 2001, p.662).
Consumption
There are L consumers in the economy, who are arranged in k non-overlapping peer groups, each of which consists of Nk consumers.
The utility of consumer i in peer group k is given by ui,kt = ln(! νqνy i,k νt) + ln(B + ! σaσ∆x i,k σt), (1)
where B > 0 (Cooper et al., 2001, p.646).
∆xi,kσt is the total difference in consumption of the status good with prestige level σ for consumer i in peer
group k. Thus, ∆xi,kσt = ! (xi,kσt − x j,k σt). (2)
Each consumer chooses the single quality of each good that has the lowest quality-adjusted price. This means that for normal goods, a consumer chooses quality ˆν for which pn
νt/qνis the lowest. For status good, she chooses
single quality ˆσ with the lowest ps
σt/aσ. ˆν and ˆσare unique and correspond to the most improved products at t 1. Then, (1) can be rewritten as:
ui,k= ln(qtyi,kt ) + ln(B + at∆xi,kt ) (3)
(Cooper et al., 2001, pp.646-647). Spending by consumer i in peer group k at time t is given by mi,k t = pn ty i,k t +pstx i,k
t . Consumers arrange themselves such that peer groups consist of consumers with identical income,
which implies that mi,k
t = mkt for all i = 1, ..., Nk. Aggregate expenditure is given by Mt=
!
kN kmk
t.2
Cooper et al. (2001) normalise prices such that nominal aggregate spending is constant each period; Mt = 1
for all t. Then, mk
t is the share in total spending of an agent in peer group k (Cooper et al., 2001, p.647).
It is further assumed that each period, consumers save a fraction s ∈ (0, 1) of their income and spend the remaining fraction 1 − s on consumption.
The only asset in the economy is a claim on future profits arising from today’s innovations, such that equi-librium savings at time t equal research expenditures in that period (Cooper et al., 2001, p.647).
Production
Final goods use labour as the only input in production, where one unit of labour produces one unit of final good, regardless of quality or prestige (Cooper et al, 2001, p.647). The cost of a unit of labour at time t is given by wt(Cooper et al, 2001, p.647). Because there is only one type of labour, this is also the cost of labour in the
R&D sector (Cooper et al, 2001, p.662).There are many firms in each sector, such that all qualities for which the patent has expired are produced as though there was perfect competition (Cooper et al, 2001, p.647). At each point in time, the labour market clears, such that
L= Dst+ Dtn+ Hts+ Htn. (4)
Research and Development
Firms can engage in R&D in an attempt to obtain a patent for a higher-quality good. The level of research employment in a sector at time t determines the probability of innovation occurring during that period, which
1The fact that the product with the lowest quality-adjusted price must also be the highest-quality product available at time t is further
explained in the section on monopoly profits.
2To avoid confusion, note that Nkmk
t is the total spending of all consumers in peer group k. Aggregate expenditure then equals the
will become available for use at t + 1 (Cooper et al, 2001, p.647). If the quantity of labour devoted to R&D in sector l = n, s is Hl
t at time t, the probability that innovation
occurs in sector l during that period is equal to φ(Hl
t) = Q(Htl)Htl, (5)
where Q(Hl
t) captures the externalities occurring due to duplication in R&D. It is assumed that Q(Htl) =
1/(Hl
t+ λ), where λ > 0 (Cooper et al, 2001, p.648).
Due to the large number of firms in each sector, individual firms take Q as given. If an innovation occurs in sector l, then a firm that devotes ε units of labour to R&D in that sector will win the patent with probability ε/Hl(Cooper et al, 2001, p.648).
Patents only last for one period, after which other firms are able to copy the new quality, such that the sector returns to a state of perfect competition. There is free entry into each R&D sector (Cooper et al, 2001, p.647).
Demand functions
Consumers in each peer group play a status game against each other in every period. At the start of a period, consumers know the available quality and price of both goods. Each consumer then chooses simultaneously how much of each good to consume (Cooper et al, 2001, p.648).
Given (3), consumers solve the following maximisation problem3:
max y,x ui,k(x i,k t , y i,k t ) s.t. mkt = pnty i,k t + pstx i,k t , (6)
which, when solving for the normal good, implies that
yi,kt = ps t(B + at !Nk j=1(x i,k t − x j,k t )) pn tat(Nk− 1) . (7)
Substitution into the budget constraint and solving for xi,k
t then gives consumer i’s reaction function, which
shows the best response to x−i,k
t , the vector of consumption choices by all others in peer group k:
Ri,kt (x −i,k t ) = mk t 2ps t − B 2at(Nk− 1) + ! j̸=ix j,k t 2(Nk− 1). (8)
The Nash equilibrium is symmetric, as consumers in the same peer group are identical, such that xi,k t = xkt
for all i = 1, ..., Nk(Cooper et al, 2001, pp.648-649), which implies that
xkt = m k t ps t − B at(Nk− 1) . (9)
It can then be obtained that xk
t = 0 is the unique Nash equilibrium when B ≥
atmkt(Nk−1)
ps
t . Thus, low
3Cooper et al. (2001) simply provide the Nash equilibrium to this problem without indicating how they arrive at this solution. This
occurs multiple times in their paper. Here, a more elaborate description of the calculation process is provided for each outcome. This is intended to provide greater clarity regarding the differences between this model and the extension of the model when similar calculations are executed in section 2.
incomes, low prestige, or high status good prices may lead to a corner solution where consumers only purchase normal goods (Cooper et al, 2001, p.648).
Thus, the demand functions of a consumer in peer group k are given by:
xkt = ⎧ ⎨ ⎩ 0; B≥ atmkt(N k−1) ps t xk t = mkt ps t − B at(Nk−1); B < atmkt(N k−1) ps t ; (10) ykt = ⎧ ⎨ ⎩ mkt pn t ; B ≥ atmkt(N k−1) ps t pst pn t B at(Nk−1); B < atmkt(N k−1) ps t . (11)
Cooper et al. (2001) focus on an economy that is affluent enough to have all peer groups k engage in some strictly positive level of conspicuous consumption in each period (Cooper et al., 2001, p.649).
This allows for the calculation of aggregate demand functions Dn
t and Dts: Dtn=!kNkytk= ps t pn t B at % kNk (Nk− 1), (12) Dts=!kNkxkt = Mt ps t −B at % kNk (Nk− 1), (13)
where, noting that Mt= 1, and defining the aggregate expenditure share as
Θ(pst, at) = pst· B at % kNk (Nk− 1), (14)
these functions can be rewritten as:
Dnt = Θ(p s t, at) pn t , (15) Dst =1 − Θ(p s t, at) ps t , (16)
where ∂Θ/∂a < 0 and ∂Θ/∂Nk <0. These demand functions are affected by a
t, but not by qt(Cooper et al.,
2001, pp.649-650).
Monopoly profits
If a firm innovates in sector l at time t−1, it becomes the only producer in that sector during period t and obtains profits πl
t= Dtl(plt− wt) (Cooper et al., 2001, p.650).
In each sector, either all firms have access to the current highest-quality product, which implies that compet-ition forces the price down to wt, or R&D activity in t − 1 results in one firm holding the patent for the current
best product. In the latter case, all other firms are one step behind on the quality ladder (Cooper et al., 2001, p.650). Thus, as the quality of the good produced in sector l is given by (γl)ι after being improved ι times,
where ι = ν, σ, the leader’s product has quality (γl)ι+1, whereas the products of other firms in the sector have
Because consumers always choose the good with the lowest quality-adjusted price, they would be indifferent between buying the leader’s product and buying the product sold by any of the other firms when wt/(γl)ι =
(pleader
t /(γl)ι+1, or equivalently, when pleadert = wtγl. Therefore, as long as the leader charges a price that is
incrementally lower than this, the firm will capture the entire market (Cooper et al., 2001, p.650). Thus:
pnt = zn twt, where znt = ⎧ ⎨ ⎩ 1 if no quality innovation at t − 1 γn if quality innovation at t − 1 , (17) pst = ztswt, where zts= ⎧ ⎨ ⎩ 1 if no prestige innovation at t − 1 γs if prestige innovation at t − 1 , (18)
There are four possible states, depending on whether or not innovation has occurred in either sector (Cooper et al., 2001, p.650).
The fact that Dt= Dtn+ Dtsimplies that
Dt= Θ(ps t, at) pn t +1 − Θ(p s t, at) ps t =Θ(p s t, at) zn twt +1 − Θ(p s t, at) zs twt . (19)
Substituting Θ into this condition and noting that ps
t = zstwt, this can be written as:
Dt= (zs t − ztn)B % kNk zn tztsat(Nk− 1) + 1 zs twt . (20)
Solving for wtthen gives
wt(zts, ztn; at) = zn tat Dtzntzstat+ (znt − zst)zstBκ , (21) where κ = ! kNk (Nk−1) (Cooper et al., 2001, p.651; 663).
Since aggregate savings must be equal to total R&D expenditures, such that S = wtHt, the wage rate can
also be expressed as wt= S/Ht= S/(L−Dt) (Cooper et al., 2001, p.663). Setting this equal to the expression
in (21) and then solving for Dtyields
Dt= zn tatL− S(ztn− zts)zstBκ zn tat(1 + ztsS) , (22)
which can be substituted into (21) to obtain wt(zts, znt, at) = zn tat(1 + ztsS) zn tzstatL+ (ztn− zts)ztsBκ . (23) Because ps t = ztswtand at = ztsat−1, Θ(pst, at) = pst· aBt ! kNk (Nk−1) = Bκwt at−1 (Cooper et al., 2001, p.663),
which, when substituting for the wage, can be expressed as: Θ(zst, ztn, at−1) = Bκzn t(1 + ztsS) zs tzntat−1L+ (ztn− zts)Bκ . (24)
taken place in either sector the previous period (Cooper et al., 2001, p.651): πtn(zs t, ztn, at−1) = Dn t zn twt (wt(znt − 1)) = Dnt & zn t − 1 zn t ' =& z n t − 1 zn t ' Θ(zs t, znt, at−1), (25) πts(zts, znt, at−1) = Ds t zs twt (wt(zts− 1)) = Dst & zs t− 1 zs t ' =& z s t − 1 zs t ' [1 − Θ(zst, ztn, at−1)]. (26)
Research intensities
R&D firms maximise expected profits, as given by QlHtl & ε Hl t ' Vtl− wtε, (27) where Vl
t is the present value of becoming the market leader at time t + 14. Because patents last for only one
period, it equals Vtl= E(π l t+1) (1 + rt) , (28)
where rtdenotes the interest rate (Cooper et al., 2001, pp.651-652).
E(πl
t+1) thus represents the expected value of being the market leader at t+1, which is dependent on whether
or not innovation has occurred in the other sector5. Thus, for the status-good sector, this is given by
E(πs
t+1) = φ(Htn)πst+1(γn, γs, at) + [1 − φ(Htn)]πt+1s (1, γs, at), (29)
while for the normal goods sector, it is equal to
E(πnt+1) = φ(Hts)πnt+1(γn, γs, at) + [1 − φ(Hts)]πnt+1(γn,1, at). (30)
Because there is free entry in the R&D sector, firms will enter until the expected profits as given in (27) are forced down to zero (Cooper et al., 2001, pp.651-652), which is true when
& Hl t Hl t+ λ ' & ε Hl t ' Vtl− wtε= ε & Vl t Hl t+ λ − wt ' = 0 ⇐⇒ V l t Hl t+ λ = wt, which implies: Vs t Hs t + λ = wt= Vn t Hn t + λ (31) 4Recall that QlHl
tis the probability of innovation by any firm in sector l and ( ε Hl
t
) is the probability of obtaining the patent given the occurrence of innovation.
